Abstract
Let R be a commutative Noetherian ring, and let N be a non-zero finitely generated R-module. The purpose of this paper is to show that N is locally unmixed if and only if, for any N-proper ideal I of R generated by ht N I elements, the topology defined by (I N)(n), n ≥ 0, is linearly equivalent to the I-adic topology.
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Acknowledgments
The authors are deeply grateful to the referee for his/her careful reading of the paper and valuable suggestions. Also, we would like to thank Professors M.P. Brodmann and S. Goto for their useful comments on Theorem 2.13.
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Presented by Michel Van den Bergh.
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Bahadorian, M., Sedghi, M. & Naghipour, R. Locally Unmixed Modules and Linearly Equivalent Ideal Topologies. Algebr Represent Theor 20, 1249–1257 (2017). https://doi.org/10.1007/s10468-017-9685-0
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DOI: https://doi.org/10.1007/s10468-017-9685-0